seminar: The equation $x+y=\alpha$ in multiplicatively dependent unknowns

speaker: Philipp Habegger (Johann Wolfgang Goethe-Universität, Frankfurt am Main)

abstract: When $\alpha$ is any non-zero algebraic number we give essentially optimal upper bounds for the height of multiplicatively dependent algebraic numbers $x$ and $y$ with $x+y=\alpha$. We improve these bounds for special values of $\alpha$ and get sharp bounds in certain cases. Finally for infinitely many $\alpha$ we show that the maximal height value obtained is isolated in a strong sense.

timetable:
Thu 7 Jul, 11:00 - 12:00, Sala Conferenze Centro De Giorgi
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